The Fraternal Birth-Order Effect as Statistical Artefact: Convergent Evidence from Probability Calculus, Simulated Data, and Multiverse Meta- Analysis

Abstract

For a quarter of a century researchers investigating the origins of sexual orientation have largely ascribed to the fraternal birth order effect (FBOE) as a fact, holding that older brothers increase the odds of homosexual orientation among men through an immunoreactivity process. Here, we triangulate the empirical foundations of the FBOE from three distinct, informative perspectives: First, drawing on basic probability calculus, we deduce mathematically that the body of statistical evidence of the FBOE rests on the false assumptions that effects of family size should be controlled for and that this could be achieved through the use of ratio variables. Second, using a data-simulation approach, we demonstrate that by using ratio variables, researchers are bound to falsely declare corroborating evidence of an excess of older brothers at a rate of up to 100%, and that valid approaches attempting to quantify a potential excess of older brothers among homosexual men must control for the confounding effects of the number of older siblings. And third, we re-examine the empirical evidence of the FBOE by using a novel specification-curve and multiverse approach to meta-analysis. This yielded highly inconsistent and moreover similarly-sized effects across 64 male and 17 female samples (N = 2,778,998), compatible with an excess as well as with a lack of older brothers in both groups, thus, suggesting that almost no variation in the number of older brothers in men is attributable to sexual orientation.

Using bootstrapping to account for sampling variation and large study bias in meta-analysis

“…We could estimate the robustness by performing random sampling from the original datasets and compare the results with the original confidence interval (i.e., 81.6% of the 1,000 ORs were within the 95% CI of the original meta-analysis). Other approaches used to assess robustness of meta-analyses include combinatorial meta-analysis, which performs meta-analysis on each possible subsample of datasets (Olkin, Dahabreh, & Trikalinos, 2012) or specification-curve and multiverse-analysis, which identifies all reasonable analysis specifications in a given study sample and compares the specification curve against the null hypothesis using parametric bootstrap (Vilsmeier, Kossmeier, Voracek, & Tran, 2021;Voracek, Kossmeier, & Tran, 2019). In addition to robustness analysis, however, our approach allows to further evaluate the impact of including more datasets, identify influential datasets, and adjust for influential datasets if necessary.…”

Increased birth rank of homosexual males: disentangling the older brother effect and sexual antagonism hypothesis

“…The generality of the FBOE has generated much recent debate fuelled by analyses of aggregated data (Blanchard, 2018c; Blanchard et al, 2021; Vilsmeier et al, 2021). Our re-analysis of all available and relevant aggregated data strongly supports the generality of the FBOE, and rejects that it is an artefact from AEs.…”

“…The fact that the expression of FBOE is fertility-dependent has a consequence for the study of FBOE. When indices are used to control for fertility, such as those proposed by Slater (1962), Berglin (1980), Blanchard (2014; 2018b; 2018c), or Vilsmeier et al (2021), the implicit assumption is that homosexual and heterosexual samples are compared independent of the mean fertility level, and the variation of those indices as a function of the mean fertility is therefore not evaluated. When the mean fertility is low (e.g.…”

“…Results using these methods indicated that FBOE was unlikely to be a sampling artefact, at least in some populations, although there is no consensus at a larger scale: several meta-analyses using an odds-ratio metric concluded that FBOE is generally present (Blanchard, 2018c, 2018c, 2018b), while a meta-analysis using another odds-ratio metric concluded that “ almost no variation in the number of older brothers in men is attributable to sexual orientation ” (Vilsmeier et al, 2021, but see Blanchard and Skorska, 2022). However, odds-ratios, and more generally all ratios, cannot be considered as reliable statistics for studying FBOE, even for non-restricted data, as this approach assumes that samples of heterosexuals and homosexuals are adequately matched for potentially confounding variables affecting sibship size, such as age or social economic status, which is not always the case (see Price and Hare, 1969).…”

Future Objectivity Requires Perspective and Forward Combinatorial Meta-Analyses

“…Nonetheless, this analysis strategy allows many human biases to be made explicitly visible at an individual studies level and meta-analyses in an unprecedented, systematic way. This has been shown by two recent applications of these approaches, both on a metameta-level: Dürlinger and Pietschnig's (2022) investigation of the association between intelligence and religiosity, and Vilsmeier et al's (2021) analysis of the stability of birth order effects.…”